# Complex Circuits

#### Circuits

Complex circuits will be the fourth and final type of method for connecting a circuit that we're looking at in chapter four. A complex circuit configuration is one that contains components that neither a parallel nor series with each other. If a circuit can be reduced to a single resistor, it is a series or parallel. If not, it is a complex circuit.

Let's look at some examples on the following slide. Here, we have four circuit types and we may want to take a little time to look at this and see if it is feasible to reduce these to a single power supply and a single resistor which would make them either a series or a parallel. If we cannot do that, then they will be a category we call a complex circuit.

On the first one, we have a power supply and we have R1, we have these components, over here … well obviously R2 and R3. We could eliminate those and that could be replaced by a single component. This replacement component and R4, those could be in parallel so it would make a single component over here. We have reduced that to R1, this component here, plus R5 at the bottom. This is a series circuit so we could reduce to, the power supply and one circuit would be the added values of these three components.

The next one, simplified. Here, we have another circuit. In this one, we see we have R1 and R7, those are obviously in series. We're going to run into some problems and our problem here would be here with R6 and R5. We wouldn't be able to solve this into a single component. I suppose that if R5 were not in the circuit or if R6 were shorted, we could reduce this. In the case the way this is drawn, it will be complex and we'll not be able to reduce it.

We have another circuit, this one, we could go in and these three components are in series so we could redo or remove these and simplify that. Here, we have a parallel. We could reduce that to one component. This component and this component would be in series so we could reduce those too and we will have this component.

Let's redraw this over here. We have this resistor coming up like this and then we have this component here. This component is connected to the power supply, and this resistor we could reduce it as well. I'll show it like to make it a little bit easier that it isn't back in parallel. These two are in parallels so we could replace that one, into a single component and so now we have a power supply in series with these two. We could add those together and we have reduced this to a power supply and one component.

This particular circuit, this is actually the Wheatstone bridge that we looked at but in the previous section it wasn't drawn like this but this is a Wheatstone bridge. R3 is the component that will make this a complex circuit. If R3... if we open this particular component, we just had R1 and R4 in series and R2 and R5 in series. Then we could look at this as in parallel with this. We could reduce this, but because R3 is here, we're not going to be able to simplify that.

In this section, we looked at the complex circuits and simplified them. Here we have the four that we started with. We found that this one, we could … this is a series parallel and that could be reduced that to a single supply in one resistor. This one we could also reduce. This one was complex; we had problems with one or either of these two components. Either we short or eliminate, we could have been … but the way it was drawn, it was complex. With D here, it was also a complex circuit because of the presence of R3.

This introduces complex circuits; we wouldn't be doing a lot of complex circuits except recognizing that they are complex circuits.